--- title: "acosh" slug: "dev-database-reference-sql-functions-numeric-acosh" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-acosh" --- > ## Documentation Index > Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt > Use this file to discover all available pages before exploring further. # acosh *Applies to VAST Cluster 5.5.* *[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Hyperbolic functions.* Returns the inverse hyperbolic cosine of a number: the value of 0 or more whose [cosh](/develop/docs/dev-database-reference-sql-functions-numeric-cosh) is that number. The argument should be 1 or more. A value below 1 doesn't raise an error: the result is `nan`. ## Syntax ``` acosh(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | Any number (`DOUBLE`, `REAL`, an integer or a `DECIMAL`) | A value of 1 or more, including `inf`. | **Returns:** `DOUBLE`, 0 or more; `nan` for an argument below 1. ## Set up the examples The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_acosh`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see. This block connects, defines the `run()` and `plan()` helpers, and creates a table of six ratios. Row 3 has no value, and row 6 is below 1, outside the range `acosh` is defined for: ``` import os import re import adbc_driver_manager import adbc_driver_manager.dbapi as dbapi import adbc_driver_vastdb BUCKET = os.environ["VASTDB_BUCKET"] SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_acosh"' conn = dbapi.connect( driver=adbc_driver_vastdb.get_driver_path(), db_kwargs={ "vast.db.endpoint": os.environ["QE_ENDPOINT"], "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"], "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"], }, autocommit=True, ) def server_message(e): """The server's message in a driver error, without the request ID or the echoed statement.""" text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e)) found = (re.search(r'message: "(.*?)", request_id', text, re.S) or re.search(r"description: (.*)\)", text, re.S)) message = found.group(1) if found else text.strip().splitlines()[-1] message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S) message = re.split(r"\\n|\n", message)[0].replace('\\"', '"') return message.replace(BUCKET, "") def run(sql): """Run one statement. Print the rows it returns, or the error.""" try: with conn.cursor() as cur: cur.execute(sql) rows = cur.fetchall() if cur.description else [] except (adbc_driver_manager.Error, OSError) as e: print(f"{type(e).__name__}: {server_message(e)}") else: print(rows) def plan(sql): """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert.""" with conn.cursor() as cur: cur.execute("EXPLAIN " + sql) steps = cur.fetchall()[0][1] print("\n".join(line for line in steps.splitlines() if "Rows" not in line)) TABLE = f"{SCHEMA}.ratios" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, x DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 2.0), (2, 1.0), (3, NULL), (4, 1.5), (5, 10.0), (6, 0.5)") ``` ``` [] [] [(6,)] ``` ## What it does `acosh(x)` is the inverse of [cosh](/develop/docs/dev-database-reference-sql-functions-numeric-cosh) for results of 0 or more: it returns the value `y >= 0` for which `cosh(y) = x`. It's 0 at 1 and grows like `ln(2x)` for large `x`, so a value as large as `1e308` gives a result of only about 710. | Call | Result | | --- | --- | | `acosh(1)` | `0.0` | | `acosh(2)` | `1.3169578969248166` | | `acosh(1e308)` | `709.889355822726` | | `acosh(0.5)` | `nan`: below 1 | The result is a `DOUBLE` for every numeric argument type: an integer, a `REAL`, a `DECIMAL` or a `DOUBLE`. ``` run("SELECT acosh(1), acosh(2), acosh(1e308), acosh(0.5)") run("SELECT typeof(acosh(1::INTEGER)), typeof(acosh(0.5::FLOAT)), typeof(acosh(0.5))") ``` ``` [(0.0, 1.3169578969248166, 709.889355822726, nan)] [('DOUBLE', 'DOUBLE', 'DOUBLE')] ``` ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `'inf'::DOUBLE` | `inf` | | `'nan'::DOUBLE` | `nan` | | Any value below 1, such as `0.9999999999`, `0`, `-0.0::DOUBLE`, `-1` or `'-inf'::DOUBLE` | `nan`, not an error | | The smallest positive `DOUBLE` (`5e-324`) | `nan` | | `'12'` (a string literal holding a number) | Converted to `DOUBLE`: `3.176313180591656` | | `'abc'` (a string that isn't a number) | Error: `Could not convert string 'abc' to DOUBLE` | | A `BLOB`, date, boolean, list or interval | Error: `No function matches the given name and argument types`, for example `'acosh(DATE)'` | The same cases, as the cluster returns them. They use the helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-acosh#set-up-the-examples): ``` run("SELECT acosh(NULL), acosh('inf'::DOUBLE), acosh('nan'::DOUBLE)") run("SELECT acosh(0.9999999999), acosh(0), acosh(-0.0::DOUBLE), acosh(-1), acosh('-inf'::DOUBLE)") run("SELECT acosh(5e-324::DOUBLE), acosh('12')") run("SELECT acosh('abc')") run("SELECT acosh(DATE '2026-10-16')") ``` ``` [(None, inf, nan)] [(nan, nan, nan, nan, nan)] [(nan, 3.176313180591656)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'acosh(DATE)'. You might need to add explicit type casts. ``` ## Examples The inverse hyperbolic cosine of each ratio. Row 6 is below 1, so its result is `nan`; [isnan](/develop/docs/dev-database-reference-sql-functions-numeric-isnan) finds those rows: ``` run(f"SELECT id, x, acosh(x), isnan(acosh(x)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 2.0, 1.3169578969248166, False), (2, 1.0, 0.0, False), (3, None, None, None), (4, 1.5, 0.9624236501192069, False), (5, 10.0, 2.993222846126381, False), (6, 0.5, nan, True)] ``` Filter on the result, and on the result with the rows below 1 left out first. Row 6 (`nan`) passes the first condition, because a `nan` result is greater than 1 in a comparison; the second leaves it out: ``` run(f"SELECT id, x FROM {TABLE} WHERE acosh(x) > 1 ORDER BY id LIMIT 10") run(f"SELECT id, x FROM {TABLE} WHERE x >= 1 AND acosh(x) > 1 ORDER BY id LIMIT 10") ``` ``` [(1, 2.0), (5, 10.0), (6, 0.5)] [(1, 2.0), (5, 10.0)] ``` ## How it runs in VAST The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `acosh()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `acosh()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `acosh()` and keeps the rows that match. No rows are skipped in storage. The plan of the first `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE acosh(x) > 1") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (acosh(x) > 1.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ x │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the raw column with the inverse of the constant.** For values of 1 or more, `acosh()` grows as its argument grows, so `acosh(x) > 1` is the same condition as `x > cosh(1)`, which also leaves out the values below 1. A function on constants is computed once, before the scan, so the second form is a comparison of the column with a constant, which is pushed down to VAST DataBase. Its plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE x > cosh(1)") run(f"SELECT id, x FROM {TABLE} WHERE x > cosh(1) ORDER BY id LIMIT 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ [(1, 2.0), (5, 10.0)] ``` - **Store the result if you filter on it often.** Compute it when you write the rows and keep it in its own column: a condition on that column is pushed down, a condition on `acosh()` isn't. ## Limitations and errors - **Below 1 gives `nan`, not an error.** Unlike [acos](/develop/docs/dev-database-reference-sql-functions-numeric-acos), [asin](/develop/docs/dev-database-reference-sql-functions-numeric-asin) and [atanh](/develop/docs/dev-database-reference-sql-functions-numeric-atanh), which fail outside their range, `acosh()` returns `nan` for any argument below 1, so the query succeeds. Leave those rows out with a pushed-down `x >= 1`, or find them with `isnan(acosh(x))`. - **Numbers only.** A `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`; the error lists the one form `acosh` has, `acosh(DOUBLE) -> DOUBLE`. A string literal is converted to `DOUBLE` if it holds a number, and otherwise fails with `Could not convert string 'abc' to DOUBLE`. - **One argument.** `acosh(1, 2)` fails with `No function matches the given name and argument types 'acosh(INTEGER_LITERAL, INTEGER_LITERAL)'`. ## Similar functions | Function | Returns | Below its range | | --- | --- | --- | | `acosh(x)` | the inverse hyperbolic cosine, for 1 or more | `acosh(0.5)` is `nan` | | [cosh](/develop/docs/dev-database-reference-sql-functions-numeric-cosh) | the hyperbolic cosine: the inverse of `acosh` | `acosh(cosh(1))` is `1.0` | | [asinh](/develop/docs/dev-database-reference-sql-functions-numeric-asinh) | the inverse hyperbolic sine, for any number | (no range limit) | | [atanh](/develop/docs/dev-database-reference-sql-functions-numeric-atanh) | the inverse hyperbolic tangent, for -1 to 1 | `atanh(2)` fails: `ATANH is undefined outside [-1,1]` | | [acos](/develop/docs/dev-database-reference-sql-functions-numeric-acos) | the inverse cosine, an angle, for -1 to 1 | `acos(2)` fails: `ACOS is undefined outside [-1,1]` | ``` run("SELECT acosh(0.5), acosh(cosh(1)), asinh(0.5)") run("SELECT atanh(2)") run("SELECT acos(2)") ``` ``` [(nan, 1.0, 0.48121182505960347)] OSError: ATANH is undefined outside [-1,1] OSError: ACOS is undefined outside [-1,1] ``` Clean up: ``` run(f"DROP TABLE IF EXISTS {TABLE}") run(f"DROP SCHEMA IF EXISTS {SCHEMA}") conn.close() ``` ``` [] [] ``` ## See also - [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric): all the numeric functions. - [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns). - [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.